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Many of the students at the International School speak [#permalink]
12 Nov 2013, 07:41

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Difficulty:

35% (medium)

Question Stats:

65% (03:58) correct
35% (01:30) wrong based on 77 sessions

Many of the students at the International School speak French or German or both. Among the students who speak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speak German do speak French. What fraction of the students speak German?

(1) Exactly 60 students speak French and German. (2) Exactly 75 students speak neither French nor German.

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Re: Many of the students at the International School speak [#permalink]
12 Nov 2013, 15:41

Expert's post

monirjewel wrote:

Many of the students at the International School speak French or German or both. Among the students who speak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speak German do speak French. What fraction of the students speak German? (1) Exactly 60 students speak French and German. (2) Exactly 75 students speak neither French nor German.

Let's say F = French only speakers G = German only speakers B = speak both N = speaker neither Four unknowns. F + G + B + N = the total population of students.

Among the students who speak French, four times as many speak German as don't --> B = 4*F

1/6 of the students who don't speak German do speak French students who don't speak German = F + N 1/6 of those are F, so N = 5*F We have two equations from the prompt that we can use with either statement.

Statement #1: Exactly 60 students speak French and German. B = 60 Therefore, F = 15 Therefore, N = 75 We have no way of calculating the value of G, so this statement, alone and by itself, is insufficient.

Statement #2: Exactly 75 students speak neither French nor German. N = 75. Therefore, F = 15 Therefore, B = 60 Again, no way of calculating G. This statement, alone and by itself, is insufficient.

Combined: Even when we combine this information, we will have no way to calculate G, so no way to answer the question. Everything together is still insufficient. Answer = (E)

Re: Many of the students at the International School speak [#permalink]
25 Mar 2014, 19:03

mikemcgarry wrote:

monirjewel wrote:

Many of the students at the International School speak French or German or both. Among the students who speak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speak German do speak French. What fraction of the students speak German? (1) Exactly 60 students speak French and German. (2) Exactly 75 students speak neither French nor German.

Let's say F = French only speakers G = German only speakers B = speak both N = speaker neither Four unknowns. F + G + B + N = the total population of students.

Among the students who speak French, four times as many speak German as don't --> B = 4*F

1/6 of the students who don't speak German do speak French students who don't speak German = F + N 1/6 of those are F, so N = 5*F We have two equations from the prompt that we can use with either statement.

Statement #1: Exactly 60 students speak French and German. B = 60 Therefore, F = 15 Therefore, N = 75 We have no way of calculating the value of G, so this statement, alone and by itself, is insufficient.

Statement #2: Exactly 75 students speak neither French nor German. N = 75. Therefore, F = 15 Therefore, B = 60 Again, no way of calculating G. This statement, alone and by itself, is insufficient.

Combined: Even when we combine this information, we will have no way to calculate G, so no way to answer the question. Everything together is still insufficient. Answer = (E)

Does all this make sense? Mike

Hi Mike Can you please explain this line to me "Among the students who speak French, four times as many speak German as don't"

Re: Many of the students at the International School speak [#permalink]
26 Mar 2014, 13:19

Expert's post

282552 wrote:

Hi Mike Can you please explain this line to me "Among the students who speak French, four times as many speak German as don't"

Dear 282552, Yes, I am happy to help.

We can divide all students who speak French into two groups Group A = those who speak French and who also speak German Group B = those who speak French but who do not speak German (Group A) + (Group B) = all students who speak French. The sentence says that (Group A) is four times bigger than (Group B). That's the meaning.

While I wasn't intending this, this is actually a sophisticated SC structure, an instance of common words dropped in parallelism. For a discussion of this topic, see: http://magoosh.com/gmat/2013/dropping-c ... -the-gmat/ Here's the sentence again with the common word included: Among the students who speak French, four times as many speak German as don'tspeak German. That's the end of the sentence.

The idiom at the beginning is also tricky --- "among [group], X is more/less/etc. than Y." By beginning with "among [group]", we are saying that we are confining our statement only to members of that group. Among Democrats, women outnumber men. Among universities in California, Stanford has the best reputation.

When the sentence begins, "among the students who speak French," we are saying that we are going to consider all French-speaking students as a single group, and completely ignore all the students who don't speak French. Inside this category of all French-speaking students, we are comparing German-speakers to non-German-speakers.

Re: Many of the students at the International School speak [#permalink]
26 Mar 2014, 17:58

mikemcgarry wrote:

282552 wrote:

Hi Mike Can you please explain this line to me "Among the students who speak French, four times as many speak German as don't"

Dear 282552, Yes, I am happy to help.

We can divide all students who speak French into two groups Group A = those who speak French and who also speak German Group B = those who speak French but who do not speak German (Group A) + (Group B) = all students who speak French. The sentence says that (Group A) is four times bigger than (Group B). That's the meaning.

While I wasn't intending this, this is actually a sophisticated SC structure, an instance of common words dropped in parallelism. For a discussion of this topic, see: http://magoosh.com/gmat/2013/dropping-c ... -the-gmat/ Here's the sentence again with the common word included: Among the students who speak French, four times as many speak German as don'tspeak German. That's the end of the sentence.

The idiom at the beginning is also tricky --- "among [group], X is more/less/etc. than Y." By beginning with "among [group]", we are saying that we are confining our statement only to members of that group. Among Democrats, women outnumber men. Among universities in California, Stanford has the best reputation.

When the sentence begins, "among the students who speak French," we are saying that we are going to consider all French-speaking students as a single group, and completely ignore all the students who don't speak French. Inside this category of all French-speaking students, we are comparing German-speakers to non-German-speakers.

Does all this make sense? Mike

Thanks Mike Nicely explained. It does make sense now!!

gmatclubot

Re: Many of the students at the International School speak
[#permalink]
26 Mar 2014, 17:58